Neural ODEs have been successfully used for short-time prediction of Burgers equation [1]}, for the evolution of dissipation in decaying isotropic turbulence [2]}, and for flow around a cylinder [3]}. Additionally, in [4]} we showed that the long-time dynamics of the KSE could be captured using neural ODEs. However, this only works when the dimension of the problem is reduced. Without any dimension reduction high wavenumbers are amplified resulting in trajectories leaving the attractor. In this work we seek to overcome this problem of high-wavenumbers amplifying not by dimension reduction, but by explicitly adding a linear term into the neural ODE approach. The properties of this linear term are described below.
